code: def asymptotic_modulation(dim, theta):
      """Compute the asymptotic modulation factor.
  
      Parameters
      ----------
      dim : int
          Dimension of the sphere (embedded in R^{dim+1}).
      theta : float
          Radius of the bubble distribution.
  
      Returns
      -------
      tuple (modulation factor, std-dev on the modulation factor)
      """
      gamma = 1.0 / dim + (1.0 - 1.0 / dim) * theta / gs.tan(theta)
      return (1.0 / gamma) ** 2
  
file_path: geomstats/examples/empirical_frechet_mean_uncertainty_sn.py
imports: import logging
  import matplotlib.pyplot
  import geomstats.backend
  from geomstats.geometry.hypersphere import Hypersphere
  from geomstats.learning.frechet_mean import FrechetMean
label_desc: Use image node_id 3 for calling a global function with example usage: asymptotic_modulation(dim, theta) and returns: unknown